Understanding Correlation in Behavioral Statistics | Introduction, Formulas & Interpretation

1. Introduction to Behavioral Statistics Correlation & Regression

2. Correlation • Introduction to Correlation & Regression • We often see things that are related to one another. • height/weight • IQ/Performance in School • Age/Income • We call this relationship Correlation • Pearson r is the most common method of measuring relationship.

3. Correlation • Formula for calculating Pearson’s r • Let x and y be two sets of paired observations with standard deviations = sx and sy • How might we measure relationship between two sets of scores?

4. Correlation How might we measure relationship between two sets of scores?

5. Correlation • Is this a good measure of relationship? • It does give different values for different degrees of relationship. • It does not provide consistency which allows it to be interpreted. • Every set of scores will yield a different score • The result will vary with the size of the scores. • How can we equalize these scores so they will give consistent and meaningful results every time?

6. Correlation • How can we equalize these scores so they will give consistent and meaningful results every time? • We can change the scores to standard scores and take the average product of the standard scores for the X and Y variables.

7. Correlation

8. Correlation • This is called the standard score formula. • It is a defining formula • It is not a formula that you would use to actually calculate the correlation coefficient. • We call this the Pearson Product Moment r

9. Pearson Product Moment Correlation Coefficient • The most widely used method of measuring correlation is the Pearson Product MomentCorrelation. • We will also consider a Rank Order Correlation Coefficient • It is an Ordinal Level Correlation Method • Spearman Rank Order Correlation • Limits for Correlation are -1 0 +1

10. Pearson Product Moment Correlation Coefficient Calculating Pearson’s Product Moment r

11. Pearson Product Moment Correlation Coefficient Example Illustrating Computation of Pearson’s r

12. Pearson Product Moment Correlation Coefficient Calculating Pearson’s Product Moment r

13. Pearson Product Moment r

14. Pearson Product Moment r • Computation of r from raw scores

15. Pearson Product Moment r Computation of r from raw scores

16. Spearman Rank Difference Correlation (Rho)(D) • Rho • We sometimes have data we want to correlate which doesn’t meet the requirements for a Pearson r. • Not at Interval Level • Rho is a correlation technique that requires only ordinal level of measurement.

17. Spearman Rank Difference Correlation (Rho)(D)

18. Spearman Rank Difference Correlation (Rho) • Advantages and Disadvantages of Rho • Advantages: • Ease of Computation • Skewness influences r but not Rho • Disadvantages: • It is somewhat less consistent from sample to sample.

19. Spearman Rank Difference Correlation (Rho) Next We will focus on interpreting a correlation coefficient and regression. Press Here to Return to CLASS PAGE